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In an isosceles right triangle ABC, with the right angle at C, the length of a leg is 20 inches. Perpendiculars are dropped from C to the hypotenuse, from the foot of this perpendicular to leg CB, from the foot if this perpendicular to AB then back to leg CB, etc..., without end. Find the sum of the lengths of all perpendiculars.

In an isosceles right triangle ABC, with the right angle at C, the length of a leg is 20 inches. Perpendiculars are dropped from C to the hypotenuse, from the foot of this perpendicular to leg CB, from the foot if this perpendicular to AB then back to leg CB, etc..., without end. Find the sum of the lengths of all perpendiculars.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.5: Inequalities In A Triangles
Problem 39E
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In an isosceles right triangle ABC, with the right angle at C, the length of a leg is 20 inches. Perpendiculars are dropped from C to the hypotenuse, from the foot of this perpendicular to leg CB, from the foot if this perpendicular to AB then back to leg CB, etc..., without end. Find the sum of the lengths of all perpendiculars.
Transcribed Image Text:In an isosceles right triangle ABC, with the right angle at C, the length of a leg is 20 inches. Perpendiculars are dropped from C to the hypotenuse, from the foot of this perpendicular to leg CB, from the foot if this perpendicular to AB then back to leg CB, etc..., without end. Find the sum of the lengths of all perpendiculars.
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